Coefficient of linear expansion of brass and steel rods are ${\mathrm{\alpha }}_1 \mathrm{and} {\mathrm{\alpha }}_2. \mathrm{Lengths} \mathrm{of} \mathrm{brass} \mathrm{and} \mathrm{steel} \mathrm{rods} \mathrm{are} {\mathrm{l}}_1 \mathrm{and} {\mathrm{l}}_2 \mathrm{respectively}.\hspace{0.17em}\mathrm{If} ({\mathrm{l}}_2-{\mathrm{l}}_1)$ is maintained same at all temperatures, which one of the following relations holds good?

• A

  ${\mathrm{\alpha }}_1{\mathrm{l}}_2 = {\mathrm{\alpha }}_2{\mathrm{l}}_1$

• B

  ${\mathrm{\alpha }}_1{{\mathrm{l}}_2}^2 = {\mathrm{\alpha }}_2{{\mathrm{l}}_1}^2$

• C

  ${{\alpha }^2}_1{l}_2 = {\alpha }_2{l}_1$

• D

  ${\mathrm{\alpha }}_1{\mathrm{l}}_1 = {\mathrm{\alpha }}_2{\mathrm{l}}_2$